I don't know. When I see a sum "c+v" relating to the speed of light I am suspicious. When that occurs there is an additional factor involved which keeps speeds below c. But my knowledge of SR is very limited.

about five to twenty minutes has elapsed — jgill

I'm glad you're not on my appointment list.

what's happening right now in a galaxy far, far way in your reference frame isn't what's happening right now in a galaxy far, far away in my reference frame. — Michael

No. Sorry. I think the difference you describe is meaningless. It certainly has no practical affect and provides no metaphysical insight.

Yes, 2.5 million years is a long time to extrapolate the orbit of our planets, but it's a pretty predictable clock nonetheless. — noAxioms

No. I think your formulation is meaningless. It has no practical affect and no metaphysical importance.

about five to twenty minutes has elapsed — jgill

I'm glad you're not on my appointment list. — Metaphysician Undercover

The time varies from 5 to 20 minutes depending upon the relative positions of the two planets.

https://mars.nasa.gov/mars2020/spacecraft/rover/communications/ :roll:

I thought you were asking how? The formula explains how. Although obviously not different universes but different reference frames.

Is that just because we don't know what is happening, or is it because there's nothing happening? A realist would presumably say that something is happening right now in a galaxy far, far way, but if special relativity is true then what's happening right now depends on our individual, relative velocities, such that what's happening right now in a galaxy far, far way in your reference frame isn't what's happening right now in a galaxy far, far away in my reference frame. — Michael

Maybe start out smaller and see if you still have a problem with it. This just extrapolates what we know happens at smaller scales and then it doesn't feel so weird at first. Take the train example. Ann is on the train, Bill is at the station. In the middle of the train is a light, which is switched off. The beam of the light is aimed at the front and the back of the train, where two identical clocks hang that are synchronised. They will stop when a light hits the sensor. The train moves at 120 km/hr. As it enters the station the light is switched on, travels through the trains and hits the clocks. Bill films this.

Ann gets off and she and Bill compare notes. Ann says, the clocks were hit simultaneously by the light and stopped at the exact same time. Bill says, that's weird, I can clearly see on my film that the light hit the back of the train before the front.

Do you feel comfortable saying both are correct because neither has a privileged frame of reference? If yes, what makes the Andromeda example different for you? If not, why not?

Sorry. I think the difference you describe is meaningless. — T Clark

You think the distinction between "there is intelligent life in the Andromeda Galaxy" being truth-apt and it not being truth-apt is a meaningless distinction?

The realist would disagree. They would argue that it's truth-apt and either true or false.

The same with something like "a fleet of spaceships has left the Andromeda Galaxy en route to Earth". It's either true or false even if we can't know which it is.

However, what's interesting about special relativity is that it seems to entail that whether or not such a proposition is true is relative to one's reference frame such that if two people cross paths in opposite directions then it can be true for one of them and false for the other. And if it's true for one of them then the future for the other is "fixed".

Do you feel comfortable saying both are correct because neither has a privileged frame of reference? If yes, what makes the Andromeda example different for you? If not, why not? — Benkei

I don't really understand your question. I certainly accept that special relativity, and its various implications such as the Andromeda Paradox, are correct, but like much of science I find it very peculiar.

I don't see anything peculiar about it. Let's assume it's Ann and Bill again, where Ann moves with 5 m/s towards the Andromeda Galaxy. To simplify it, they are immortal, the earth and the Andromeda Galaxy are at a fixed distance of 25 million lightyears from each other and Ann can just walk through space. While Bill stays put, Ann moves toward the light coming towards her showing the events as they unfold. Of course she's going to see the decision to invade Earth before Bill does. By the time the light reaches her, she's simply closer to it. She's been walking millions of years towards it already. Once Bill sees the decision happening, for Ann at that point, having walked at 5 m/s for all that time, the light reaching her then is 15 days later and the armada is already on its way.

I thought you were asking how? The formula explains how. Although obviously not different universes but different reference frames. — Benkei

Thanks.

You think the distinction between "there is intelligent life in the Andromeda Galaxy" being truth-apt and it not being truth-apt is a meaningless distinction? — Michael

Although I've seen it used before, I wasn't familiar with the term "truth-apt," so I looked it up - "A sentence is truth apt if there is some context in which it could be uttered (with its present meaning) and express a true or false proposition." To start, that doesn't seem like a very interesting characterization for any statement. I also don't see how it applies in this context.

While Bill stays put, Ann moves toward the light coming towards her showing the events as they unfold. Of course she's going to see the decision to invade Earth before Bill does. By the time the light reaches her, she's simply closer to it. She's been walking millions of years towards it already. Once Bill sees the decision happening, for Ann at that point, having walked at 5 m/s for all that time, the light reaching her then is 15 days later and the armada is already on its way. — Benkei

But the relativity of simultaneity isn't just about one person seeing something before another person; it's about that thing actually happening for one person before another person. That's what I find peculiar.

I also don't see how it applies in this context. — T Clark

A statement such as "a fleet of spaceships has just left the Andromeda Galaxy en route to Earth" is either true or false, even though we don't, and can't, know which.

The "common sense" realist view is that if it's true then it's true for all of us, otherwise it's false for all of us, but if special relativity is correct then whether or not it's true can be relative to our individual movements.

The "common sense" realist view is that if it's true then it's true for all of us, otherwise it's false for all of us, but if special relativity is correct then whether or not it's true can be relative to our individual movements. — Michael

Sorry. It seems trivial. Philosophers sitting around the campfire making up spooky stories, flashlights under their chins. Not that there's anything wrong with that.

https://en.m.wikipedia.org/wiki/Rietdijk–Putnam_argument — Michael

About the Rietdijk–Putnam argument, to which the above link refers to, we read the following:
"In philosophy, the Rietdijk–Putnam argument, named after C. Wim Rietdijk [nl] and Hilary Putnam, uses 20th-century findings in physics – specifically in special relativity – to support the philosophical position known as four-dimensionalism."

This reference is among those that can entrap you in an endless nested chain of references within references, as they contain terms that you are not acquainted with and you need to look them up. Even if you can skip some of them, there some that are important for the understanding of the subject at hand. In this case, we have the term "four-dimensionalism". So, from Wikipedia, I read the following:

"In philosophy, four-dimensionalism (also known as the doctrine of temporal parts) is the ontological position that an object's persistence through time is like its extension through space. Thus, an object that exists in time has temporal parts in the various subregions of the total region of time it occupies, just like an object that exists in a region of space has at least one part in every subregion of that space." (https://en.m.wikipedia.org/wiki/Four-dimensionalism)

Now, I had to look up temporal parts, because it is central to the description of four-dimensionalism. It is also an intriguing term, I think:
"In contemporary metaphysics, temporal parts are the parts of an object that exist in time. A temporal part would be something like 'the first year of a person's life', etc."
But can a person's life be considered an "object"? And if we accept that to be true, should we also consider thoughts as objects too? But both are concepts that cannot exist in space! How can we include them in 4 dimensions when they do not exist even in 3 dimensions? See the impasse one could get in? Well, this might be \a problem of mine only ...

However, getting back to the description of four-dimensionalism, there are things that throw me off or, at best, make me wonder:
1) "An object's persistence through time is like its extension through space". But if something (physical) exists a) it exists in space, where else? and b) if something exists (in space) can it not exist in time too?
(And, what does "extension through space" mean? This is too perplexing,)
2) "An object that exists in time has temporal parts in the various subregions of the total region of time it occupies." We say that an object occupies space. I really cannot see how it can also "occupy time". Can time be occupied? If it could, then we wouldn’t be able e.g. to hear two sounds together! It would like in the early computers that could only produce monophonic sounds. So, I am wondering, is occupying time just a ridiculous notion or there's something more to it?

This is as far as the Rietdijk–Putnam argument is concerned. I will reply to the Andromeda Paradox in a separate comment.

Your statement assumes a privileged frame of reference. It's not coherent within the context of relativity theory.

Your statement assumes a privileged frame of reference. — Benkei

Which statement?

Sorry. It seems trivial. Philosophers sitting around the campfire making up spooky stories, flashlights under their chins. Not that there's anything wrong with that. — T Clark

Especially if those spooky stories illuminate special relativity in such challenging ways. :roll:

Is it a paradox or is it an inconsistency in what domain expressions quantify over?

1 ) Event X has occurred at time u in Alice's reference frame.
2 ) Event X has occurred at time v in Bob's reference frame.
Plus:
ROS ) u isn't necessarily equal to v.

There isn't any ambiguity there. Or a contradiction. There would be a contradiction if you add:

3 ) All events have a unique time of occurrence.

Or a variant like:

4 ) Every event's outcome is fixed at some time t.

Both ( 3 ) and ( 4 ) go against the "relativity of simultaneity" concept. The unique time of occurrence in ( 3 ) fixes a time in all reference frames (thus necessary equality), which contradicts relativity of simultaneity. The fixed time in ( 4 ) does the same, as it is unique (thus necessary equality).

That uniqueness isn't of a numerical value, since 2 is always 2, that uniqueness construes each event as indexed by a unique time in a shared index set. Relativising time, as an index set of events, to a reference frame is a core posit of special relativity. The "paradox" is just premise smuggling through ambiguous phrasing. ( 1 ) and ( 2 ) quantify within a reference frame's set of time points, 3 and 4 quantify over both index sets.

Edit: or alternatively, it provides a neat demolition of our pre-theoretical space and time intuitions. They don't represent how nature really works.

But the relativity of simultaneity isn't just about one person seeing something before another person; it's about that thing actually happening for one person before another person. That's what I find peculiar. — Michael

Before and after are relative to the frame of reference. So if the two persons are of the same frame of reference, then the event will not happen for one person before the other person. And, if they are of different frames of reference it makes no sense to talk about it "happening for one person before another person" because before and after are frame dependent. That is why it is sometimes necessary to use a "world line", or "proper time", to make sense of such an idea.

I think this is unnecessarily pedantic.

In one person’s reference frame the event is in the present (or past), and in the other person’s reference frame the event is in the future. I find this peculiar.

And, for the purpose of the Andromeda Paradox, it shows that the second person’s future is inevitable.

it's about that thing actually happening for one person before another person. — Michael

See my response to MU here.

You think it's peculiar that in a setup where event A follows B, where one person moves towards those events, that person will see A before the other person, where for both observers those events and their sequence are set by the parameters of the setup? The past, present and future are set by the setup for both, the simultaneity is merely a consequence of their relative velocity but neither has any effect on the sequence of events. Observation by the first person has zero consequences for the second person.

You think it's peculiar that in a setup where event A follows B, where one person moves towards those events, that person will see A before the other person — Benkei

No. This has nothing to do with what one person sees. There are distant events happening in my present that I cannot see because they are too far away. According to special relativity some of these events happen in your future even though they are happening in my present. This is what I find peculiar.

No. This has nothing to do with what one person sees. There are distant events happening in my present that I cannot see because they are too far away. According to special relativity some of these events happen in your future even though they are happening in my present. This is what I find peculiar. — Michael

In Special Relativity, an observer can be identified with an inertial reference frame in which they are at rest, and relative to which they make all their space and time measurements. This can be likened to a set of co-moving rods and clocks, all synchronized by light signals. For instance, Clocks A and B can be synchronized through a light signal sent back and forth between them, with the time at Clock B being set at the mid-point interval between the departure and return times at Clock A. Consequently, two observers can have different simultaneity planes due to the fact that events are timed with reference to distinct sets of clocks that have been synchronized differently. @Benkei's train example above illustrates this concept well.

Actual "observers" (such as human beings) are free to choose whatever reference frames they want, and can translate space-time coordinates of events using the Lorentz transformations. So long as they reside outside of their light cones, the issue of events being located in their "relative past" or "relative future" doesn't have any physical or metaphysical significance. It only has relevance to the degree that it challenges certain presentist or "growing block universe" conceptions of time. This was Putnam's main point in his paper, "Time and Physical Geometry".

However, getting back to the description of four-dimensionalism, there are things that throw me off or, at best, make me wonder:
1) "An object's persistence through time is like its extension through space". — Alkis Piskas

In addition to the problematic objects, there is also the question of what to do with the uniqueness of observers.

What the Andromeda Paradox implies is that the observed universe apparently shifts in its entirety towards a moving observer. Which means that in the forward moving direction many more of the most distant galaxies come into possible view and we lose some distant galaxies from possible view behind us. This is all pretty absurd, yet it is demonstrably true.

Then this becomes equivalent to an observer shifting its 'present' physically measurably in space toward the direction of motion. The effect is that we can see from some future present some event that can then be prevented from causing harm in the present present after we quickly got back to where we belong.

What the Andromeda Paradox implies is that the observed universe apparently shifts in its entirety towards a moving observer. Which means that in the forward moving direction many more of the most distant galaxies come into possible view and we lose some distant galaxies from possible view behind us. This is all pretty absurd, yet it is demonstrably true. — magritte

The galaxies you are moving towards would have come into view regardless of your motion, only at a later time as measured by your clock. Similarly, the galaxies you are moving away from will also come into view, but at a later time. In a flat spacetime, you cannot indefinitely outrun light rays. Interestingly, as you acquire more velocity relative to both sets of galaxies, they "move" closer to you due to the effects of Lorentz contraction.

However, as you gain speed, the reason why the light from the galaxy behind you doesn't catch up to you sooner (despite the contracted distance) is due to the recalibration of your plane of simultaneity. As this occurs, the photons that were a distance D away before you started moving suddenly "jump" back in time and are "now" less advanced on their journey towards you!

What the Andromeda Paradox implies is that the observed universe apparently shifts in its entirety towards a moving observer. — magritte

I have not tackled the Andromeda Paradox yet. In the articles it is said to be an extension by Penrose of "a form of" the Rietdijk–Putnam argument. I only talked about the Rietdijk–Putnam argument itself and how it didn't make much sense to me.

So I expected that the OP would clarify at least one or two of my questions. The OP however couldn't care less. Well, there are different ways OPs view and handle their launching of a discussion ...

Afer that, I couldn't care less myself about the Andromeda Paradox, But since you have brought it up, I just had a look on it, in the same article of the link in question.

My first impression is that the "experiment" is unnecessary complex and includes unnecessary details that add nothing to its essence, e.g. the two persons crossing each other --because it is impossible to pass each other ... except if they were foot racing! :grin: They could be anywhere on the planet. The "paradox" has to do mainly with time, and very little with space. Then the trip to Andromeda is too far-fetched and quite unrealistic. The same "paradox" could be set on something much simpler and realistic, like e.g. tennis final. (One can think of a million of such simple examples.) So, one person knows that the match is about to start and the other doesn't know what time the match will start. One can add more uncertainties --always realistic ones-- e.g. wheher the match will take place at the foreseen day or it will be postponed because of weather conditions, which players are going to compete for the title, etc.

Which means that in the forward moving direction many more of the most distant galaxies come into possible view and we lose some distant galaxies from possible view behind us. This is all pretty absurd, yet it is demonstrably true. — magritte

I see that you introduce more factors than what is described by Penrose. But this can be done also in my own example as I mentioned above. However, the main factor --as I see it-- involved here, the "protagonist", is "uncertainly". Any additions only increase --they might also decrease-- that uncertainty.

Then this becomes equivalent to an observer shifting its 'present' physically measurably in space toward the direction of motion. The effect is that we can see from some future present some event that can then be prevented from causing harm in the present present after we quickly got back to where we belong. — magritte

You see a factor here the importance or even the meaning of which --in the present context-- most probably escapes me: the direction of motion.

Well, It;s good that at least you enjoy this "paradox"! :smile: